For the same reason many complex desktop applications use sqlite or some other database.

My use case is an offline-capable app. There was already WebSQL, but it got deprectaed.

It depends on you use case but, for example, if your db is not super large you could dowload it and use it locally istead of having to connect to an app server for every query or transaction. You could synchronize in the background with the app server. The app speed and responsiveness would be way better.

Or maybe you could use a sqlite replication tool in the browser for near realtime changes in the master node db.

And for single user apps developped with tools like Electron having your db engine in the browser makes the app faster and life easier for the dev.

Node as app server and db backend for a single user app is inefficient, slow and resource hogging.

Using Sqlite you could get rid of node and therefore, reduce memory usage, speed up app loading and execution, have a single code base in the browser that makes debugging far easier, reduce code complexity and app size, reduce cpu cycles, energy usage and CO2 emissions, save precious life time, etc... :-)